Related papers: Characterizing Model Spaces Among the Finite Dimen…
We consider the notion of finite dimensional reconstructions systems (RS's), which includes the fusion frames as projective RS's. We study erasures, some geometrical properties of these spaces, the spectral picture of the set of all dual…
We study reproducing kernel Hilbert spaces (RKHS) on a Riemannian manifold. In particular, we discuss under which condition Sobolev spaces are RKHS and characterize their reproducing kernels. Further, we introduce and discuss a class of…
A unitarily invariant, complete Nevanlinna--Pick kernel $K$ on the unit ball determines a class of operators on Hilbert space called $K$-contractions. We study those $K$-contractions that are constrained, in the sense that they are…
In this paper, we have considered vector valued reproducing kernel Hilbert spaces (RKHS) $\mathcal{H}$ of entire functions associated with operator valued kernel functions. de Branges operators $\mathfrak{E}=(E_- , E_+)$ analogous to de…
The performance of adaptive estimators that employ embedding in reproducing kernel Hilbert spaces (RKHS) depends on the choice of the location of basis kernel centers. Parameter convergence and error approximation rates depend on where and…
We use the multiplicative structure of the Koszul resolution to give short and simple proofs of some known estimates for the total dimension of the cohomology of spaces which admit free torus actions and analogous results for filtered…
We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2 . The class includes, as a special case, the usual empirical norm…
Based on the theory of reproducing kernel Hilbert space (RKHS) and semiparametric method, we propose a new approach to nonlinear dimension reduction. The method extends the semiparametric method into a more generalized domain where both the…
This note finds a new characterization of complete Nevanlinna-Pick kernels on the Euclidean unit ball. The classical theory of Sz.-Nagy and Foias about the characteristic function is extended in this note to a commuting tuple $\bfT$ of…
In this paper, we present sharp estimates for the covering numbers of the embedding of the reproducing kernel Hilbert space (RKHS) associated with the Weierstrass fractal kernel into the space of continuous functions. The method we apply is…
This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…
We call the solution of a kind of second order homogeneous partial differential equation as real kernel alpha-harmonic mappings. In this paper, the representation theorem, the Lipschitz continuity, the univalency and the related problems of…
This paper presents a general coding method where data in a Hilbert space are represented by finite dimensional coding vectors. The method is based on empirical risk minimization within a certain class of linear operators, which map the set…
Finite element spaces by Whitney $k$-forms on cubical meshes in $\mathbb{R}^n$ are presented. Based on the spaces, compatible discretizations to $H\Lambda^k$ problems are provided, and discrete de Rham complexes and commutative diagrams are…
Let H be an infinite-dimensional (real or complex) Hilbert space, viewed as a metric structure in its natural signature. We characterize the definable linear operators on H as exactly the "scalar plus compact" operators.
This paper generalizes regularized regression problems in a hyper-reproducing kernel Hilbert space (hyper-RKHS), illustrates its utility for kernel learning and out-of-sample extensions, and proves asymptotic convergence results for the…
We show that minimum-norm interpolation in the Reproducing Kernel Hilbert Space corresponding to the Laplace kernel is not consistent if input dimension is constant. The lower bound holds for any choice of kernel bandwidth, even if selected…
The persistence of excitation (PE) condition is sufficient to ensure parameter convergence in adaptive estimation problems. Recent results on adaptive estimation in reproducing kernel Hilbert spaces (RKHS) introduce PE conditions for RKHS.…
A persistence diagram is a finite multiset of birth-death pairs representing the lifetimes of topological features across a filtration. Persistence diagrams do not carry intrinsic spectral or kernel structures, so applications typically use…
We introduce a family of reproducing kernel Hilbert spaces $\mathcal A_\Lambda$ of holomorphic functions defined on an infinite--dimensional domain in a separable Hilbert space, $\mathbb{H}$. The reproducing kernel of $\mathcal A_\Lambda$…